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Timestepping schemes for the 3d Navier-Stokes equations

Hong, Y-J; Wirosoetisno, D

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Authors

Y-J Hong



Abstract

It is well known that the (exact) solutions of the 3d Navier–Stokes equations remain bounded for all time if the initial data and the forcing are sufficiently small relative to the viscosity. They also remain bounded for a finite time for arbitrary initial data in L2. In this article, we consider two temporal discretisations (semi-implicit and fully implicit) of the 3d Navier–Stokes equations in a periodic domain and prove that their solutions remain uniformly bounded in H1 subject to essentially the same respective smallness conditions as the continuous system (on initial data and forcing or on the time of existence) provided the time step is small.

Citation

Hong, Y., & Wirosoetisno, D. (2015). Timestepping schemes for the 3d Navier-Stokes equations. Applied Numerical Mathematics, 96, 153-164. https://doi.org/10.1016/j.apnum.2015.05.006

Journal Article Type Article
Acceptance Date May 3, 2015
Online Publication Date Jun 5, 2015
Publication Date Jun 5, 2015
Deposit Date Sep 29, 2016
Publicly Available Date Sep 13, 2017
Journal Applied Numerical Mathematics
Print ISSN 0168-9274
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 96
Pages 153-164
DOI https://doi.org/10.1016/j.apnum.2015.05.006

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